Movement of material particles in a conical hopper

The movement of material particles in a conical hopper was investigated using the variational principle to determine their trajectory. A mathematical model based on minimizing the energy of particle flows  (“streamlines”) was developed, which allowed calculating the angular coordinates and velocity projections of the particles. After experimental verification of the model, it was possible to use the obtained results to optimize the organization of continuous flow of material from a conical hopper depending on the design parameters of the latter, for example, during storage and transportation of cement.